Question

Find the value of `81^(3/4) - (1/32)^((-2)/5) + 8^(1/3) (1/2)^-1 (4)^0`

Answer 1

Given,

`81^(3/4) - (1/32)^((-2)/5) + 8^(1/3) (1/2)^-1 (4)^0`

We need to simplify the given terms.

Thus, `81^(3/4) - (1/32)^((-2)/5) + 8^(1/3) (1/2)^-1 (4)^0`

⇒ `(3^4)^(3/4) - (1/2^5)^((-2)/5) + (2^3)^(1/3) xx (1/2)^-1 xx 1`  ...[∴ a⁰ = 1 where a ≠ 0]

⇒ `(3)^(4 xx 3/4) - (2^-5)^((-2)/5) + (2)^(3 xx 1/3) xx (2^-1)^-1`  ...`[∴ a^-n = 1/a^n, (a^m)^n = a^(mn)]`

⇒ (3)³ – (2)² + (2) × 2

⇒ 27 – 4 + 4

⇒ 27

Hence, `81^(3/4) - (1/32)^((-2)/5) + 8^(1/3) (1/2)^-1 (4)^0 = 27`.